Pre-flight design assessment and validation of navigation systems require emulating data acquired by a range of different hypothetical configurations of onboard sensors with different quality standards and/or sampling time specifications. A proper validation procedure requires the emulated data to be available at arbitrarily specified sampling times and for different hypothetical test-trajectories. The problem thus formulated entails obtaining, for the different case studies, closed solutions of the nonlinear kinematics equations as explicit functions of time. The method proposed is based on constructing a subset of the solutions of the kinematics equations contained in a vector spline functional space whose order may be arbitrarily specified. Particular consideration is devoted to the solutions of the attitude quaternion. The method is illustrated with experimental data obtained during a sub-orbital flight of the VS30 vehicle of the Brazilian Space Agency.Fil: Giribet, Juan Ignacio. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaFil: España, Martin Dario. Universidad de Buenos Aires; ArgentinaFil: Miranda, Carlos. Universidad de Buenos Aires; Argentina